Adults randomly selected for a poll were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of the subjects surveyed, 464 were in favor, 431 were opposed, and 139 were unsure. A politician claims that people don't really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin flip. Use a 0.05 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician's claim? Find the null and alternative hypotheses. O A. Ho: P = 0.5 OB. Ho: P#0.5 H1: p > 0.5 H1 : p = 0.5 O C. Ho: P = 0.5 OD. Ho: P = 0.5 H1 : p 18 ug/g OD. Ho: H = 18 ug/g H1: H 18 ug/g e the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Ho. There is evidence to conclude that the mean lead concentration for all such medicines is 18 pg/g.A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts (a) and (b) below. Height (cm) of President 188 173 169 177 189 178 Height (cm) of Main Opponent 179 180 173 168 181 174 a. Use the sample data with a 0.01 significance level to test the claim that for the population of heights for presidents and their main opponents, the differences have a mean greater than 0 cm. In this example, ud is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the president's height minus their main opponent's height. What are the null and alternative hypotheses for the hypothesis test? Ho: Hd cm H1: Hd cm (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the P-value is the significance level, the null hypothesis. There sufficient evidence to support the claim that presidents tend to be taller than their opponents. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? The confidence interval is | cm